I had one the exact same way. Hole in ball, everything. I screwed the puller back in. Put in some powder from the flash hole and pushed the ball on to the powder. It came out just fine.

If you don't want to use powder or the CO2 thingy, a blow gun with a rubber tip pressed tight against the nipple works pretty good. First plug the holes with one of the mentioned methods - I lean toward screwing the puller back in. (I usually keep my compressor set at around 100 psi.)

Oops, I forgot you're working with a flinter. Next time get it stuck in a percussion rifle.